CAIE S1 2016 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2016
SessionJune
TopicNormal Distribution
TypeExpected frequency with unknown parameter

5 The heights of school desks have a normal distribution with mean 69 cm and standard deviation \(\sigma \mathrm { cm }\). It is known that 15.5\% of these desks have a height greater than 70 cm .
  1. Find the value of \(\sigma\). When Jodu sits at a desk, his knees are at a height of 58 cm above the floor. A desk is comfortable for Jodu if his knees are at least 9 cm below the top of the desk. Jodu's school has 300 desks.
  2. Calculate an estimate of the number of these desks that are comfortable for Jodu.